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Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
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Force appropriation of nonlinear structures.

L Renson1, T L Hill1, D A Ehrhardt1

  • 1Dynamics and Control Research Group, University of Bristol, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 7, 2018
PubMed
Summary
This summary is machine-generated.

Nonlinear normal modes (NNMs) can be inaccurately identified using the common quadrature condition, especially with single-force excitation. Energy transfer analysis reveals when this method fails, suggesting optimal excitation strategies for accurate nonlinear system dynamics. Keywords: nonlinear normal modes, experimental identification, quadrature condition, structural dynamics.

Keywords:
energy transferforce appropriationnonlinear dynamicsnonlinear normal modesphase quadrature

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Area of Science:

  • Mechanical Engineering
  • Structural Dynamics
  • Nonlinear Dynamics

Background:

  • Nonlinear normal modes (NNMs) are crucial for modeling and understanding nonlinear structures.
  • Experimental identification of NNMs often relies on a phase quadrature condition.
  • Single-input force excitation is a common practical approach in experimental modal analysis.

Purpose of the Study:

  • To investigate the accuracy of the phase quadrature condition for identifying NNMs.
  • To analyze the impact of single-force excitation on NNM identification.
  • To propose improved methods for accurate NNM identification in nonlinear structures.

Main Methods:

  • Studied a clamped-clamped cross-beam with closely spaced modes.
  • Applied a single input force for excitation.
  • Analyzed energy transfer between system modes.
  • Evaluated the phase quadrature condition's accuracy.

Main Results:

  • The commonly used quadrature condition can yield significantly different results from true NNMs.
  • Inaccuracies are pronounced with single-force excitation.
  • Energy transfer analysis helps predict regions of quadrature condition inaccuracy.
  • The study highlights limitations of the quadrature condition in specific scenarios.

Conclusions:

  • The phase quadrature condition is not universally accurate for NNM identification, particularly with limited excitation.
  • Energy transfer analysis provides insights into the limitations of the quadrature method.
  • Optimal excitation strategies, including the number and location of input forces, are critical for accurate NNM identification.